Fluid milk is the most important product of Norwegian agriculture, and the decline in milk purchase has impact in many rural communities. By decomposing the milk purchase into cohort effects, age effects and year effects we show that the reason for the decline is that older generations purchase more milk than younger generations, and during lifetime consumption decline with age. Consequently, as younger generations replace older generations milk purchase decline. We show that towards 2021 the milk purchase will continue to fall.Milk, Purchases, Cohorts, Food Consumption/Nutrition/Food Safety,

Gustavsen, Geir Waehler

Rickertsen, Kyrre

English

Research Papers in Economics

  1 
12
th Congress of the European Association of Agricultural Economists – EAAE 2008 
Consumer Cohorts and Milk Purchases 
 
Gustavsen G.W. 
1 and Rickertsen K. 
1,2 
1 Norwegian Agricultural Economics Research Institute, Oslo, Norway  
2 University of Life Sciences/Department of Agricultural and Resource Economics, AAs, Norway 
Abstract— Fluid milk is the most important product 
of Norwegian agriculture, and the decline in milk 
purchase has impact in many rural communities. By 
decomposing the milk purchase into cohort effects, age 
effects and year effects we show that the reason for the 
decline is that older generations purchase more milk 
than younger generations, and during lifetime 
consumption decline with age. Consequently, as younger 
generations replace older generations milk purchase 
decline. We show that towards 2021 the milk purchase 
will continue to fall.  
Keywords— Milk, Purchases, Cohorts 
I. INTRODUCTION 
Norwegians are heavy milk drinkers, however, the 
consumption of fluid milk has declined steadily over 
the last twenty years.  Over the period 1986 to 2006, 
the per capita purchases of fluid milk were reduced by 
more than a third.  This reduction has partly been 
offset by increased consumption of cheeses and some 
other diary products but the total milk production 
declined about 15% over the period according to the 
Norwegian Agricultural Economics Research Institute, 
NILF [1, 2].   
Milk is the most important product in Norwegian 
agriculture, and about one third of total income comes 
from dairy production.  Although agriculture only 
contributes to 2.6% of the total employment, dairy 
production is important in many rural areas and 
reduced production affects rural communities across 
the country.  Consequently, the demand for fluid milk 
is important for the future of these communities. 
Several studies have investigated the Norwegian 
demand for fluid milk. Rickertsen [3] found an own-
price elasticity of -0.27 and a total expenditure 
elasticity of 0.54 using annual data for 1962 – 1991 
period.  Using data for 4-months
 observation periods 
for the years 1978 – 2001, Gustavsen and Rickertsen 
[4] found that the own-price elasticity and total 
expenditure elasticities had been reduced to –0.14 and 
–0.03, respectively.  Using the same data set but for 
the 1975 – 1995 period, Rickertsen and Gustavsen [5] 
found that the own-price elasticities of whole milk and 
low-fat milk were -0.14 and -0.68, respectively, while 
the own-advertising elasticity for fluid milk was found 
to be 0.0008.  The estimated differences in numerical 
values may, at least, partly be explained by different 
sample periods and differences in the model 
specifications.  In any case, the general conclusion 
from these studies is that the aggregate demand for 
fluid milk is quite inelastic with respect to changes in 
the price of milk, advertising, and income.  These 
inelastic values suggest that economic factors alone 
cannot fully explain the observed decline in fluid milk 
consumption and reliably forecast future consumption. 
The inelastic demand responses corresponds generally 
well with studies in other countries.  For a summary of 
such results; see for example Rickertsen and 
Gustavsen [5].   
To provide additional insights, we use an alternative 
modelling strategy and follow cohorts of households, 
where the cohorts are defined by the age of the head of 
the household.  We follow Deaton [6] and decompose 
purchases of milk into age, cohort, and year effects.  
Age effects make older individuals purchase 
differently than younger individuals regardless of 
cohort and year.  Cohort effects make individuals from 
different generations purchase differently regardless of 
age and year.  Year effects make the purchases of all 
age groups and all cohorts vary between years.  Year 
effects may be explained by special events in specific 
years or changes in the economic conditions that 
affects all cohorts and age groups.  Expected milk 
consumption for a specific age group, in a specific 
cohort, and in a specific year is found by adding the 
effects. The total effect of age, cohort, and year may 
resemble a trend and trend variables (e.g., Rickertsen 
and Gustavsen [5] and Gustavsen and Rickertsen [4] 
or habit persistence (e.g. Rickertsen [3]) have   2 
12
th Congress of the European Association of Agricultural Economists – EAAE 2008 
frequently been introduced into demand systems to 
improve the fit and forecasting abilities of the models.   
To distinguish between age, cohort, and year effects 
may improve the explanatory power of the model and 
increase the reliability of forecasts of future purchases 
of milk. For example, assume that an age variable, but 
no cohort variables, is included in the model and a 
positive age effect is found. This effect could be 
explained in different ways.  First, it could be 
explained by increased health awareness among older 
individuals leading to more healthy drinking habits 
and increased purchases of milk.  If this explanation is 
true, then an increased average age of the population 
will result in increased future aggregate purchases.   
However, the effect could alternatively be explained 
by cohort effects where older cohorts purchase more 
than younger.  Cohort effects could be explained by 
historical experiences.  After the Second World War, 
milk was considered to be an important part of any 
healthy diet.  However, the nutritional value of milk 
has been questioned and milk’s nutritional status has 
declined among younger generations.  If the latter 
explanation is true, then the replacement of older with 
newer generations will result in decreased future 
aggregate purchases.  To further investigate these 
alternative scenarios, we follow Deaton [6] and create 
pseudo panels of household data.  Using these pseudo 
panels, we construct cohort–year pairs and decompose 
the milk purchases into age, cohort, and year effects. 
II. AGE, COHORT, AND YEAR EFFECTS 
  We decompose milk purchases as 
QA C Y u β αγψ =+ + + +                                  (1)   
where Q is the stacked vector of cohort–year pairs, A 
a matrix of age dummies, C a matrix of cohort 
dummies, and Y a matrix of year dummies.  The 
cohort data are arranged as cohort–year pairs, with 
each observation corresponding to a single cohort in a 
specific year.  If there are n such cohort–year pairs, the 
three matrices will each have n rows.  The number of 
columns will be the number of age groups, the number 
of cohorts, and the number of years, respectively.   
Each row corresponds to a single observation of the 
logarithm of the average milk purchases of a cohort 
group in a specific year.  Because each of the matrices 
is singular, we have to drop one age dummy, one 
cohort dummy, and one year dummy from the 
estimation.  Furthermore, there exists an additional 
linear relationship across the three matrices.  If we 
know the year of an observation and when the 
observed cohort was born, then we can infer the age of 
the cohort.  We follow Deaton [6, p. 126] and impose 
the orthogonality restriction  0, sψ ′ = where ψ  is the 
parameter vector of the year effects in equation (1), 
and  s  = (0, 1, 2, …, 15) is a trend where s = 0 
represents the year 1986 and s = 15 represents the year 
2001.  The year dummies in the Y matrix are redefined 
to 
*
21 [( 1) ( 2) ] tt yy t y t y =−− −−  for t  = 3, …, 15, 
where  t y  is the year dummy that is equal to 1 if the 
year is t and zero otherwise.  This procedure enforces 
the restriction  0 sψ ′ =  and, furthermore, the restriction 
that the year effects have to sum to zero.   
III. DATA AND EMPIRICAL IMPLEMENTATION 
  The household expenditure surveys cover the 
1986–2001 period and are described in Statistics 
Norway [7].  In the surveys, the country is divided into 
sampling areas corresponding to the more than 400 
counties of Norway.  These sampling areas are 
grouped in 109 strata, and a sample area is randomly 
drawn from each stratum.  Sampling areas are drawn 
with a probability proportional to the number of 
persons living in the area.  Next, persons are randomly 
drawn from the 109 sampling areas such that the 
sample becomes self-weighting.  When a person is 
drawn, the household of that person is included.   
Finally, these households are randomly drawn to 
record their expenditures in one of the 26 two-week 
survey periods of the year.  Each year 2,200 persons 
are initially drawn.  The non response rate varies 
between 33 and 52 percent and our total sample 
consists of about 20,500 cross-sectional observations. 
The household expenditure surveys are repeated 
every year and we follow cohorts of households.  The 
cohorts are defined by the age of the head of the 
household.  Our oldest cohort was between 58 and 62 
years old in 1986.  For simplicity, we refer to the age 
of this cohort as 60 years old in 1986, 61 years old in 
1987, up to 75 years old in 2001.  This cohort was   3 
12
th Congress of the European Association of Agricultural Economists – EAAE 2008 
around twenty years old by the end of the Second 
World War.  Correspondingly, we define eight 
additional cohorts who were 55, 50, 45, 40, 35, 30, 25, 
and 20 years old in 1986.  In 1991 we added the cohort 
group who was between 18 and 22 years old in that 
year, and in 1996 we added the cohort group who was 
between 18 and 22 years old in that year.  In total, 11 
cohort groups were defined in 2001. For example, the 
cohort born in 1961 was 25 years old in 1986, 35 years 
old in 1996, 40 years old in 2001, and will be 60 years 
in 2021. The cohort born in 1961 were 25 years in 
1986, the cohort born in 1966 were 25 years old in 
1991, the cohort born in 1971 were 25 years old in 
1996, and so on. 
The average per capita purchases of households 
with a head aged 25 years old were 134 litres in 1986, 
120 litres in 1991, 92 litres in 1996, and 56 litres in 
2001.  At this age, older generations purchased more 
milk than younger generations did, i.e., cohort effects.  
Furthermore, there are substantial age effects.  For all 
cohorts, milk purchases decline with age.  A 
household born in 1966 purchased 124 litres per capita 
in 1986, i.e. when the head was 20 years old.  15 years 
later, in 2001, a corresponding household purchased 
76 litres per capita, i.e., a 39% reduction.  A household 
born in 1926 purchased 146 litres per capita in 1986 
and 107 litres in 2001, i.e., a 27% reduction.  For all 
cohorts, there are similar declines with age in milk 
purchases.  These age effects are a natural part of 
getting older.  In general, older people use less energy 
than younger people, hence they consume less milk. 
For each cohort–year pair, we computed the natural 
logarithm of the average milk purchases per capita 
weighted by the inverse of the probability of 
participating in the survey.  Following Deaton [6, p. 
124], we assumed away interaction effects between 
age, cohort, and years, and decomposed logarithm of 
milk purchases into age, cohort, and year effects. 
IV. RESULTS 
  We estimated equation (1) using ordinary least 
squares.  The first age dummy and the first cohort 
dummy were dropped from estimation, so the age 
effects are compared with a household with head aged 
20 years old and the cohort effects are compared with 
the cohort where the head of the household was 20 
years old in 1996.  The year dummies for 1986 and 
1987 were dropped from the estimation, but recovered 
from the adding-up and orthogonality restrictions.   
The regression results show that all the age and 
cohort effects, and some of the year effects, are 
significantly different from zero and the R
2 is 0.85. 
The age effects are relative to a household with a head 
aged 20 years old, and the cohort effects are relative to 
the cohort born in 1976. The age, cohort and year 
effects are reproduced in figure 1. The age effects 
show the expected difference in the logarithm of milk 
purchases between a 20-year-old person and persons 
of other ages, regardless of generation or year.   
Likewise, the cohort effects show the expected 
differences in the logarithm of milk purchases for each 
generation compared to the generation born in 1996, 
disregarding age and year.  In reality we cannot 
disregard age, cohort, or year, because there exists an 
exact linear relationship between these variables.  An 
individual has to belong to a generation, have an age 
and make purchase in a year.   
The upper left panel of figure 1 shows the 
development of the logarithm of milk purchases of the 
different cohorts over time.  For clarity of exposition 
just six of the 11 cohorts are shown, but the pattern is 
similar for the other cohorts as well.  The top line 
shows the oldest cohort while the bottom short line 
shows the youngest cohort.  The other cohorts are in 
between.  Several effects are evident from this panel.  
First, there are substantial cohort effects.  The line for 
an older cohort is always above the lines for a younger 
cohort when they are observed at the same age.  As 
mentioned above, these cohort effects may be 
explained by historical experiences.  The generations 
who grew up around the Second World War often 
suffered from food shortages and milk was an 
important nutritional element.   
The upper right and the two lower panels of figure 1 
show the age, cohort, and year effects.  These effects 
are the coefficients of equation (1) where the year 
effects are restricted to sum to zero.  So the age effect 
is the difference in log of milk purchases between a 
20-year-old person and persons of other ages.  The 
cohort effects are the difference of log of milk 
purchases between the cohort born in 1976 and other 
cohorts.  The year effects vary around zero.  The age 
effects are negative and the cohort effects are positive   4 
12
th Congress of the European Association of Agricultural Economists – EAAE 2008 
and both effects are of similar magnitudes.  The older 
a person is, the less milk that person buys. Moreover, 
the older a cohort is, as compared with the cohort born 
in 1976, the more milk a person belonging to that 
cohort buys.  The year effects are very small compared 
with the other effects. 
 
Figure 1. Milk purchases by cohorts and their           
Decomposition 
Milk purchases by cohorts
3.9
4.4
4.9
20 40 60 80
Age in years
L
o
g
 
o
f
 
l
i
t
e
r
s
Age effects
-2
-1.5
-1
-0.5
0
20 40 60 80
Age in years
L
o
g
 
o
f
 
l
i
t
e
r
s
 
Cohort effects
0
0.5
1
1.5
2
2.5
02 0 4 0 6 0 8 0
Cohort: Age in 1986
L
o
g
 
o
f
 
l
i
t
e
r
s
Year effects
-0.1
-0.05
0
0.05
0.1
1985 1990 1995 2000 2005
Year
L
o
g
 
o
f
 
l
i
t
e
r
s
 
V. TREND EXTRAPOLATIONS 
Using the results in figure 1, we can find the 
expected milk purchase for a given age, cohort, and 
year as 
2 ˆ ˆˆ ˆ ˆ 0.5 ˆ (| ,, )
ii j j kk AC Y EQ ACY e
β αγ ψ σ ++ + + ∑ ∑∑ =     (2) 
where the last term in the exponential is the 
standard error of the residuals.  This correction factor 
has to be included because we take the expectation of 
an exponential (Miller [8]). This extrapolation for 
three different cohorts in 2021 is shown in table 1 
Table 1. Milk purchases in selected cohorts and years 
Cohort born 
 
2001 
Litres 
2021          Diff 
 Litres          % 
1939-1943  108  85               -21 
1954-1958    95  56               -41 
1969-1973    75  41               -45 
________________________________________________ 
   5 
12
th Congress of the European Association of Agricultural Economists – EAAE 2008 
The cohorts not shown in table 1 have the same 
pattern as those shown in table 1. In all cohorts the 
purchase is expected to continue declining towards 
2021 because positive cohort effects and negative age 
effects. And this may aggravate the problems of the 
rural communities most dependent upon agriculture. 
VI. CONCLUSIONS 
  The positive effect on purchases of increasing age 
has sometimes been attributed to increased health 
awareness among older people.  However, the results 
of our cohort analysis suggest that older generations 
purchase more than younger generations while age by 
itself has a negative impact on milk purchases.  A 
household will purchase less milk as it gets older, but 
still purchase more than an identical household from a 
younger generation.  The replacement of generations 
will continue and further decreases in milk purchases 
are likely.  Decreasing milk purchases are likely to 
reinforce the problems of agriculture and many rural 
communities. 
REFERENCES 
1.  NILF (2001) Norwegian agriculture: Status and 
trends. Norwegian Agricultural Economics 
Research Institute. Oslo, Norway 
2.  NILF (2007) Norwegian Agriculture: Status and 
Trends. Norwegian Agricultural Economics 
Research Institute. Oslo, Norway 
3.  Rickertsen K (1998) The demand for food and 
beverages in Norway. Agric Econ 18: 89-100 
4.  Gustavsen G W, Rickertsen, K (2003) 
Forecasting ability of theory-constrained two 
stage demand systems. Europ Rev of Agric 
Econ 30:539–558 
5.  Rickertsen K, Gustavsen G W (2002)  Fluid 
milk consumption and demand response to 
advertising for non-alcoholic beverages. 
Agricultural and Food Science in Finland 
11:13–26 
6.  Deaton A (1997) The analysis of household 
surveys: A microeconometric approach to 
development policy. Baltimore MD: The Johns 
Hopkins University Press 
7.  Statistics Norway (1996) Survey of Consumer 
Expenditure 1992–1994. Oslo–Kongsvinger: 
Official statistics of Norway 
8.  Miller D M (1983) Reducing transformation 
bias in curve fitting. The American Statistician 
38:124–126 
 
•  Corresponding author:  Geir Waehler Gustavsen 
•  Institute:  Norwegian Agricultural Economics    
              Research Institute (NILF)  
•  Street:  Storgata 2-4-6 
•  City:  Oslo 
•  Country:  Norway   
•  Email:  geir.gustavsen@nilf.no   
 

Fluid milk consumption and demand response to advertising for non-alcoholic beverages. Agricultural and Food Science in

Forecasting ability of theory-constrained two stage demand systems.

Norwegian Agriculture: Status and Trends. Norwegian Agricultural Economics Research Institute.

Reducing transformation bias in curve fitting.

Survey of Consumer Expenditure 1992–1994. Oslo–Kongsvinger: Official statistics of Norway

The analysis of household surveys: A microeconometric approach to development policy. Baltimore MD: The Johns Hopkins

The demand for food and beverages in Norway.

Consumer Cohorts and Milk Purchases

Consumer Cohorts and Milk Purchases

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